When she says, at the end, that "the world needs Gossip Girl", she's entirely right, and she is taking up an important social function by taking up the role. Selflessly, too, since we can see the toll it takes on her personal and social life.
It's been very well established by now that these people are above the law - getting away with murder, little more than a slap on the wrist for framing a man for rape and having him imprisoned for a decade, and having lackeys at several levels of law enforcement, from police to prosecutors to judges, working for them. They are, literally, untouchable.
You can't hurt them monetarily, either. The poorest of our main characters is Blair Waldorf, and she has paid servants, can fly around the world on a whim, and generally doesn't worry about money.
So, you take away the law and money, and what's left of accountability? By what mechanism can these people be held responsible for their actions? Status. They're aspiring business leaders and socialites and authors and politicians. They live and die by their image and how other people see them.
You can't count on the mainstream media to transmit their behaviour to the world with any fidelity, however. The largest gossip rag in New York, the Spectator, is owned and edited by Nate, one of their own. They invite and schmooze and buy the affections of the mainstream gossip journalists, like the Post's Page Six, by inviting them to their lavish parties with open bars. The mainstream media is much more likely to be part of a coverup than an exposé.
So one girl stands alone and serves as a check on these fucking teenagers' worst instincts. When Serena tries to keep it in her pants, or Blair forgives her enemies, or Chuck doesn't murder the prostitutes he hires, it's for one reason only: they know Gossip Girl will be there to document every moment.
Gossip Girl got taken out of commission by the group earlier this winter, and that was a huge threat to the social order. Without her, there's little to keep New York City from becoming Gotham at the hands of these spoiled teenage assholes.
So, yes, thank you, Georgina, for being a hero, taking up the Gossip Girl mantle, and taking one for the team.